3. Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. (a) f(x) = x² + 7 – x, a = 4 ||

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Q: (b) f(x) - (x + 2x')', a- -1

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A: the soluton is following.

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Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: 2. For the given function, f, determine if the function is discontinuous at a given point. State…

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A: Given function is, f(x)=(x+2x3)4, a=-1

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Q: Find the limit and discuss the continuity of the function.

A: Evaluate lim(x,y)→(2,4)x+yx2+1

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Q: Let f (x) = 2Vx + 1. Find f'(x), carefully evaluating the limit.

A: Given : f(x) = 2x+1 Using first principle of differentiation we get  f'(x)=limh→0 f(x+h)−f(x)h

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Q: 10. Prove that the statement "If lim f(r) exists, then f is continuous at a" is false by using a…

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Q: x5 – x4 – 2x3 f(x) = x4. х4 — Зх3 — х2 + 3х x2 + 3x

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.